Mathematics
Average / Arithmetic Mean
Two groups have averages 30 and 50. If the combined average is 38, what is the ratio of their sizes (first:second)?
A. 2:3
B. 4:5
C. 3:2
D. 5:4
Correct Answer: C
Ratio = (50−38):(38−30)=12:8=3:2.
Mathematics
Average / Arithmetic Mean
The average of 7 numbers is 30. If one number 42 is removed, what is the average of the remaining numbers?
A. 26
B. 30
C. 28
D. 32
Correct Answer: C
Total 210; remaining total 168; 168/6=28.
Mathematics
Average / Arithmetic Mean
A class average rises from 60 to 62 when a new student scoring 90 joins. How many students were originally in the class?
A. 14
B. 12
C. 18
D. 16
Correct Answer: A
60n+90=62(n+1), so n=14.
Mathematics
Average / Arithmetic Mean
A batsman needs an average of 50 after 20 innings. After 19 innings his average is 48. What must he score in the 20th innings?
A. 92
B. 90
C. 86
D. 88
Correct Answer: D
Required total 1000; current total 912; needed 88.
Mathematics
Average / Arithmetic Mean
The average of five consecutive odd integers is 51. What is the sum of the smallest and largest integers?
A. 106
B. 100
C. 102
D. 104
Correct Answer: C
Terms are 47,49,51,53,55; endpoints sum to 102.
Mathematics
Average / Arithmetic Mean
A team of 11 players has average age 26 years. A 32-year-old player is replaced by a 21-year-old player. What is the new average age?
A. 27 years
B. 23 years
C. 29 years
D. 25 years
Correct Answer: D
Total decreases by 11; mean decreases by 1 to 25.
Mathematics
Average / Arithmetic Mean
The mean of 9 numbers is 24. Eight of them have mean 22. What is the ninth number?
A. 42
B. 44
C. 38
D. 40
Correct Answer: D
Total 216; first eight total 176; ninth = 40.
Mathematics
Average / Arithmetic Mean
The average of 12 numbers is 18. If each number is doubled and then 5 is added to each, what is the new average?
A. 43
B. 45
C. 41
D. 39
Correct Answer: C
New mean = 2×18+5 = 41.
Mathematics
Average / Arithmetic Mean
Two varieties cost Rs. 380/kg and Rs. 435/kg. In what ratio should the cheaper be mixed with the dearer to obtain an average cost of Rs. 350/kg?
A. 17:-6
B. 18:-6
C. -6:17
D. 17:-5
Correct Answer: A
By allegation, cheaper:dearer = (435−350):(350−380) = 17:-6.
Mathematics
Average / Arithmetic Mean
Two varieties cost Rs. 360/kg and Rs. 420/kg. In what ratio should the cheaper be mixed with the dearer to obtain an average cost of Rs. 340/kg?
A. -1:4
B. 4:-1
C. 4:0
D. 5:-1
Correct Answer: B
By allegation, cheaper:dearer = (420−340):(340−360) = 4:-1.
Mathematics
Average / Arithmetic Mean
Two varieties cost Rs. 340/kg and Rs. 405/kg. In what ratio should the cheaper be mixed with the dearer to obtain an average cost of Rs. 330/kg?
A. 16:-2
B. 15:-1
C. 15:-2
D. -2:15
Correct Answer: C
By allegation, cheaper:dearer = (405−330):(330−340) = 15:-2.
Mathematics
Average / Arithmetic Mean
Two varieties cost Rs. 320/kg and Rs. 390/kg. In what ratio should the cheaper be mixed with the dearer to obtain an average cost of Rs. 320/kg?
A. 1:0
B. 0:1
C. 1:1
D. 2:0
Correct Answer: A
By allegation, cheaper:dearer = (390−320):(320−320) = 1:0.
Mathematics
Average / Arithmetic Mean
Two varieties cost Rs. 300/kg and Rs. 375/kg. In what ratio should the cheaper be mixed with the dearer to obtain an average cost of Rs. 310/kg?
A. 2:13
B. 14:2
C. 13:2
D. 13:3
Correct Answer: C
By allegation, cheaper:dearer = (375−310):(310−300) = 13:2.
Mathematics
Average / Arithmetic Mean
Two varieties cost Rs. 280/kg and Rs. 360/kg. In what ratio should the cheaper be mixed with the dearer to obtain an average cost of Rs. 300/kg?
A. 4:1
B. 3:1
C. 3:2
D. 1:3
Correct Answer: B
By allegation, cheaper:dearer = (360−300):(300−280) = 3:1.
Mathematics
Average / Arithmetic Mean
Two varieties cost Rs. 260/kg and Rs. 345/kg. In what ratio should the cheaper be mixed with the dearer to obtain an average cost of Rs. 290/kg?
A. 6:11
B. 11:7
C. 12:6
D. 11:6
Correct Answer: D
By allegation, cheaper:dearer = (345−290):(290−260) = 11:6.
Mathematics
Average / Arithmetic Mean
Two varieties cost Rs. 240/kg and Rs. 330/kg. In what ratio should the cheaper be mixed with the dearer to obtain an average cost of Rs. 280/kg?
A. 4:5
B. 5:5
C. 6:4
D. 5:4
Correct Answer: D
By allegation, cheaper:dearer = (330−280):(280−240) = 5:4.
Mathematics
Average / Arithmetic Mean
Two varieties cost Rs. 220/kg and Rs. 315/kg. In what ratio should the cheaper be mixed with the dearer to obtain an average cost of Rs. 270/kg?
A. 9:11
B. 9:10
C. 10:9
D. 10:10
Correct Answer: B
By allegation, cheaper:dearer = (315−270):(270−220) = 9:10.
Mathematics
Average / Arithmetic Mean
Two varieties cost Rs. 200/kg and Rs. 300/kg. In what ratio should the cheaper be mixed with the dearer to obtain an average cost of Rs. 260/kg?
A. 3:3
B. 2:4
C. 3:2
D. 2:3
Correct Answer: D
By allegation, cheaper:dearer = (300−260):(260−200) = 2:3.
Mathematics
Average / Arithmetic Mean
A group of 21 people has average 45. Two people aged 34 and 39 leave, and two aged 54 and 59 join. What is the new average?
A. 46.9
B. 47.9
C. 45.9
D. 48.9
Correct Answer: A
Adjust the unchanged-size group's total, then divide by 21. New mean = 46.9.
Mathematics
Average / Arithmetic Mean
A group of 20 people has average 44. Two people aged 33 and 38 leave, and two aged 53 and 58 join. What is the new average?
A. 46
B. 47
C. 45
D. 48
Correct Answer: A
Adjust the unchanged-size group's total, then divide by 20. New mean = 46.